Between November 1 and January 31, Connecticut residents can register for health insurance for 2017 at any time. During the rest of the year, you need a qualifying event--such as a marriage or new job--to register. If you want your coverage to begin January 1, you must register by December 15.

Jim Wadleigh, the CEO of Access Health, acknowledged that some residents will see a big increase in their premium rates, but not everyone.

"You are seeing, not only in Connecticut, rates are increasing, but your seeing it across the country. There are no real spots that have been immune to the rapidly rising healthcare costs across the country. It's an issue that at a state level we have to work on, and at a federal level needs to be worked on as well," Wadleigh said.

In October, the Obama administration announced that premiums under the Affordable Care Act would see as much as double-digit rate hikes for 2017. Access Health CT is the marketplace for Connecticut for residents to adhere to the requirement for healthcare under Obamacare if they don't get insurance through work or a spouse.

And that will impact some Connecticut residents, but there are some ways to get around the issue.

"There are a number of our customers that will see double-digit rate increases," Wadleigh said, but he also said "there are a number of our customers that won't. And so some of the differences, nuances of that really comes down to this thing called financial help. So, about 75 percent of the Access Health customers receive financial help, and what that means is in the form of tax credits, some of their premiums are being offset. That, in turn, when rates go up that financial help goes up as well."

Since some insurance carriers have left the exchange, only Anthem and ConnectiCare remain. Wadleigh recommends that when picking your insurance, you check with your current doctors to see if they take one or the other so that you don't have to change physicians.